Phonon Lifetime and Lattice Thermal Conductivity of the I-Alpdmn Icosahedral Quasicrystal

The lattice thermal conductivity of the icosahedral i-AlPdMn phase is very similar to the one of glasses with an umklapp peak that is replaced by a broad plateau in the temperature range 20 to 300 K and a value of the thermal conductivity of the order 1-2 wK -1 m -1 in this temperature range [1]. This is also very similar to what is found in structurally complex materials such as Ge based clathrates for instance [2]. Several explanations have been given for this behaviour. The first one is a generalised umklapp process, related to the existence of several pseudo-Brillouin zone boundaries in a quasicrystal acting as Bragg plane reflexion [3]. On the other hand, in the context of structurally complex materials, a simple model was designed, pointing out to the restricted energy range for which acoustic modes do exist [4], following an idea of Slack [5]. Since in quasicrystal the acoustic regime is also restricted [6; 7], this model could be extended to quasicrystals. However, testing those predictions requires the measurement of phonon dispersion together with phonon lifetime, a challenging task from the experimental point of view. Recently using the neutron resonant spin-echo technic, we have found surprisingly large phonon lifetime and phonon mean free path in the Ge-Ba-Au clathrate, contradicting the ‘phonon glass’ picture usually associated to such materials [2]. Indeed close to the Brillouin zone boundary and for transverse